I have come across this comment that seems to say there is a globally accepted definition of reskinning and refluffing and that it's not the same thing (I thought it was).
What are the commonly accepted definitions of reskinning and refluffing?
I don’t think there are any “commonly-accepted” definitions of the term. Some (e.g. SevenSidedDie in the linked comment, AceCalhoon in a comment to Jonathan’s answer) make a distinction between the two terms, while others (e.g. Jonathan himself, leokhorn in asking the question, and mxyzplk in a comment to Jonathan’s answer) make no distinction and feel that what the first group is terming as “reskinning” as distinct from “refluffing” is neither of these things, but rather some form of very-small-scale homebrew.
I don’t think you can therefore rely on any distinction to be made by anyone reading your use of “reskinning,” but you also cannot rely on people not making some distinction – some people will assume you’re making one and others will assume you’re not. It seems safer to use “refluffing” since the definition of “fluff” is pretty consistent, though what counts as fluff and what counts as crunch definitely does vary somewhat, thanks to many publishers not officially denoting one versus the other. E.g. some people may consider it a rule that barbarians come from some relatively-primitive tribal culture, while others may consider that fluff and find the barbarian’s mechanics (e.g. some form of berserk frenzy ability) appropriate to “refluff” for drastically different characters (the same bonuses may also be fitting for a kind of “zen focus” or even “bullet time” depending on the system). So all around, your mileage may vary. It’s probably best to be thorough in your descriptions to avoid these problems.
So far as I've seen them used, they both mean the same thing.
There is at least a commonly accepted definition of fluff: everything that has no influence or substance in the mechanics. Fluff can be removed altogether or replaced with no consequence to the workings of the system, and usually comes in the form of story and description. Its counterpart, crunch, covers everything that has purely mechanical substance and which, if altered or removed, would alter the mechanics at play at some point.
"Refluffing" has always been about changing the fluff of something to give it a new look and feel, whilst keeping the mechanical designs intact. "Reskinning" has always been about... the exact same thing.
When it comes to changing the mechanics, that has different terms, such as homebrewing.